The role of the induction zone on the detonation–turbulence linear interaction

Abstract

Detonation–turbulence linear interaction analysis extends the non-reactive shock–turbulence analog by considering geometrical scaling of the noise with respect to the half-reaction distance. The analysis emphasizes the effect of structure in energizing selective frequencies, and determining acoustic amplification in the farfield. Natural frequencies are determined as eigenvalues of the inviscid non-forced interaction problem. They modify postshock energy spectra by supporting resonant amplification, and cast light on the role of the activation energy on the detonation–turbulence interaction. Detonations with higher activation energies amplify smaller scales by resonant amplification. An analysis of the bifurcation parameters reveals a strong link between detonation overdrive and acoustic attenuation. The damping is correlated with the subcritical nature of the characteristic solutions for high overdrives. For detonation conditions on the stability boundary, a larger overdrive supports a weaker resonant peak in both the temperature and longitudinal velocity spectra. Postshock temperature variances feature a well-defined maximum within the reaction zone, which is found to be sensitive to changes in detonation structure.

Keywords:

• detonation
• linear interaction analysis
• shock-turbulence interaction
• detonation instability
• turbulence

Notes

¹The location of the minimum imaginary part of the radial and longitudinal wavenumber eigenvalues agree within two significant digits, thus the radial wavenumber is chosen to identify the minimum.